four in Line

Strategy and fun

Current status

Red Token Turn
LOGIDIAS Interactive Module

Four in a Row: Game Theory & Minimax Algorithm

Educational & Scientific Guide

🔬 Scientific & Physical Foundations

Four-in-a-row board simulation illustrating combinatorial game theory and Alpha-Beta minimax pruning.

🕹️ User & Experimentation Guide

Click columns to drop game tokens and challenge progressive depth-searching AI bots.

Frequently Asked Questions (FAQ)

Is four-in-a-row a mathematically solved game?

Yes, in 1988 James Allen proved the first player can always force a win with perfect play.

How does the AI choose moves?

Evaluates game decision trees projecting multiple turns ahead using the Minimax algorithm.

What is Alpha-Beta pruning?

An optimization that prunes subtrees that cannot affect final decision values, saving computations.

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Minimax Search Tree vs. Alpha-Beta Pruning Complexity Calculator

📄 Open Solved Worksheet & Guide ➔
🎓 Elementary & Middle School Logic🎓 High School CS & AI Algorithms Mathematical Principle & Governing Equations: NMinimax = bd  ──(α-β Pruning)──▶  Noptimal ≈ bd/2
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🎯 3 Self-Grading Practical Challenges (Instant Verification)

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#1.On a standard 7×6 Connect 4 board, what did Victor Allis mathematically prove in 1988 regarding perfect play?
#2.How does Alpha-Beta (α-β) pruning improve the Minimax algorithm without changing its chosen move?
#3.Why is the center column strategically dominant on a 7-column Connect 4 grid?